A chicken model is constructed in the following manner. Assume that consumers like chickens, and also that the private sector cannot produce chickens, but the government can. Therefore, it would be efficient for the government to produce chickens. Randy Wright tells me (confirmed by Richard Rogerson) that this parable originates with Ed Prescott.
The trick in any serious policy analysis is to write down a coherent economic model with a role for the government that is not a chicken model. We have all seen chicken models from time to time. My favorite is IS/LM, where the "chicken" is price flexibility and/or wage flexibility.